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Rapid mixing of quantum spin chains at any finite temperature — arXiv:2610.01190

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01190
License (as archived): CC0-1.0
Archived: 2026-10-07T11:37:43.215Z
SHA-256 of the archived text: 29fb544daad4421fb9a1733989902341ec37c42eb8988a92fe4ff4186693275c
Stable URL of this page: https://metraipolis.com/documento/dc_28f5dd68bfca

How to cite

Rapid mixing of quantum spin chains at any finite temperature — arXiv:2610.01190 — arXiv (en), https://arxiv.org/abs/2610.01190 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_28f5dd68bfca (Metraipolis archive dc_28f5dd68bfca, sha256 29fb544daad4421fb9a1733989902341ec37c42eb8988a92fe4ff4186693275c)

BibTeX

@misc{dc28f5dd68bfca,
  title = {Rapid mixing of quantum spin chains at any finite temperature — arXiv:2610.01190},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01190},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_28f5dd68bfca; sha256 29fb544daad4421fb9a1733989902341ec37c42eb8988a92fe4ff4186693275c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01190. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove that a quasi-local quantum Gibbs sampler rapidly mixes to the Gibbs state of any 1D finite-range Hamiltonian at all finite temperatures in $\mathcal{O}\left(\log (n/\varepsilon)\right)$ time. Each update traces out a contiguous block of constant length and reconstructs it using the Petz recovery map, following early proposals for quantum heat-bath Gibbs samplers by Kastoryano and Brandão~\cite{kastoryano2016quantum}. Our proof directly bounds the distance between the updated state and the target Gibbs state using quantum Wasserstein distance of order $1$. We further provide $\mathcal{O}(\text{polylog}(n/\varepsilon))$ depth of quantum circuits to prepare these Gibbs states. We hope these techniques will facilitate the analysis and design of other Gibbs samplers.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.01190 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:19:01.680Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).